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Symmetry-breaking bifurcations of the uplifted elastic strip

G.Domokos
Department of Strength of Materials and Center for Applied Mathematics and Computational Physics,
Budapest University of Technology and Economics

W.B. Fraser
School of Mathematics and Statistics,
The University of Sydney

and

I. Szeberenyi
Department of Information Technology,
Budapest University of Technology and Economics

Abstract

We investigate the global equilibria of the uplifted heavy elastic strip. We show that after nondimensionalization the problem is parameter-free and find stable and physically observable configurations which break the reflection symmetry of the initial shapes. We derive the Hamiltonian for this system that is valid even after frictionless self-contact has occurred. This also resolves the apparent overdetermination of the boundary conditions for the fully nonlinear problem. After showing that symmetry-breaking always precedes self-contact, we carry the computations beyond self-contact and compare the results qualitatively with experimental observations. The equilibria are identified numerically by a global search algorithm, capable of finding disconnected solutions. The consistent application of this method enables us to find nonsmooth branches of equilibria producing generalized bifurcations.





Szeberenyi Imre 2005-10-08